Discrete element modelling of frac sand crushing under one-dimensional compression using PFC2D

Wenbo Zheng

In the proceedings of: GeoVancouver 2016: 69th Canadian Geotechnical Conference

Session: FUNDAMENTALS - IX Physical & Numerical Modelling

ABSTRACT: Hydraulic fracturing of tight shales which enhances the fracture conductivity typically uses frac sand consisting of quartzgrains to prop the fracture open.However,the sand can be crushed by high compressive stress acting on the fractures.This reduces the fracture conductivity. This paper presents the results of discrete element modelling of sand crushingtests usingParticleFlow Code (PFC2D).The main purpose isto calibrate numerical models of sand under highcompressive stresses usinglaboratory crushing test data.A particle breakage algorithm incorporatinggrain-sizedependent particlestrength and failure mechanismundershearing conditionwasimplemented andevaluatedin PFC2D.One-dimensional compression tests on an assembly of particles with a uniform grain size distribution over a narrowrange of grain sizes are simulated with maximum compressive stresses of 20, 30, and 40 MPa. The contact forces onindividual particles are converted to equivalent stresses, which in turn, are used to determine if a particle breaks.Whenthe state of stress acting on an individual particle reachesaparticle breakage criterion, particle crushing is representedby replacing the overloaded particle by anarray of smaller particles in the model.The papercompares laboratory crushtest data with the numerical simulations and demonstrates how incorporation of particle breakage algorithms can allowthePFC2Dmodel to capture the change in particle size distribution as well as the non-linear stress-strain response ofsand under high compressive stresses.R•SUM•La fracturation hydraulique pour am†liorer la conductivit† de la fracture de schistes argileux serr†s utilise g†n†ralementfrac sable constitu† de grains de quartz pour maintenir la fracture ouverte. Cependant, le sable peut ‡tre †cras† par uneforte contrainte de compression agissant sur les fractures. Ceci r†duitla conductivit† de la fracture. Cet article pr†sentles r†sultats de la mod†lisation des †l†ments discrets de tests de broyage de sable … l'aide de Particle Flow Code(PFC2D). Le but principal est de calibrer les mod—les num†riques de sable sous des contraintes de compression †lev†esen utilisant des donn†es de test de laboratoire de concassage.Les algorithmes incorporentm†canismes de r†sistanceet d'†chec particules d†pendant granulom†trie sous traction ou de cisaillement conditions. Essais de compression … unedimension sur un assemblage de particules avec une distribution uniforme de la taille des grains sur une gamme †troitede tailles de grains sont simul†s avec des contraintes de compression maximales de 20, 30 et 40MPa. Les forces decontact sur les particules individuelles sont converties en contraintes †quivalentes qui, … leur tour, sont utilis†es pourd†terminer s–il y seraitune rupture de particules. Lorsque l'†tat de contrainte agissant sur une particule individuelleatteint un crit—re de rupture des particules de broyage de particules est repr†sent† par le remplacement de la particulesurcharg†e par un r†seau de petites particules dans le mod—le.Cet articlecompare les donn†es de test en laboratoired'†crasement avec les simulations num†riques et d†montre comment l'incorporation d'algorithmes de bris de particulespeut permettre au mod—le PFC2Dpour capturer le changement dans la r†partition de la taille des particules, ainsi que lar†ponse contrainte-d†formation non-lin†aire de sable sous fortes contraintes de compression..1INTRODUCTIONFrac sand is widely used as aproppant for hydraulicfracturingto increase the recovery rate of hydrocarbons intheoil and gas industry.After hydraulic fracturing, asandpack isformed between fracturesto resist the closurestress and prop open fractures, which act as paths for oiland gas to flow.However, the high closure stresswithinthe hydraulic fractures often crushessandgrains intosmaller fragments (Palisch et al. 2009). Sand crushingreduces the fracture aperture and the void ratio of thesand pack. The presence of small fragments of crushedsand greatly decreases the permeabilitybyblockinghydrocarbonflow paths.In current practice for frac sand selection, the ISO13503-2 standardis usedformeasuringthe percent offines generated due to crushing under a certaincompression stress. Another standard uses a conductivitycell with proppant embedded between two fracture facesto measure fracture conductivity (Rivers et al. 2012). Fordifferent formationsunder different closure stress,manytests are needed to select an optimal proppant, which isvery time consuming and requireslarge specializedtesting equipment.The discrete element method(DEM)has been used tosimulate particle breakage under static compression(Hosseininia andMirghasemi 2006, Refahi et al. 2010, DeBono andMcDowell 2014).This paperusesa two-

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